Decimals on a Number Line Worksheets | Updated June 2022 - Free Printable

Problem Analysis:

The task involves identifying the decimal values of points \( P \), \( Q \), and \( R \) on given number lines. Each number line is divided into segments, and we need to determine the decimal value corresponding to each marked point based on the divisions.

Solution Approach:

1. Understand the Scale: Each number line is divided into equal segments. The length between two consecutive whole numbers (e.g., 0 to 1, 1 to 2) is divided into a certain number of equal parts. The value of each segment can be calculated by dividing the distance between two whole numbers by the number of segments.

2. Locate Points: Identify the position of points \( P \), \( Q \), and \( R \) relative to the whole numbers and the segments.

3. Calculate Decimal Values: Use the scale to determine the exact decimal value for each point.

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Detailed Solutions:

#### Number Line 1:
- Given Values:
- \( P = 0.2 \)
- \( Q = 0.8 \)
- \( R = 1.5 \)

This number line is already solved and serves as an example.

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#### Number Line 2:
- Scale: The distance between 0 and 1 is divided into 10 equal segments. Each segment represents \( 0.1 \).
- Points:
- \( P \): Located 4 segments after 0.
\( P = 0 + 4 \times 0.1 = 0.4 \)
- \( Q \): Located 7 segments after 1.
\( Q = 1 + 7 \times 0.1 = 1.7 \)
- \( R \): Located 9 segments after 1.
\( R = 1 + 9 \times 0.1 = 1.9 \)

Answers:
- \( P = 0.4 \)
- \( Q = 1.7 \)
- \( R = 1.9 \)

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#### Number Line 3:
- Scale: The distance between 1 and 2 is divided into 5 equal segments. Each segment represents \( 0.2 \).
- Points:
- \( P \): Located 2 segments after 1.
\( P = 1 + 2 \times 0.2 = 1.4 \)
- \( Q \): Located 3 segments after 2.
\( Q = 2 + 3 \times 0.2 = 2.6 \)
- \( R \): Located 4 segments after 2.
\( R = 2 + 4 \times 0.2 = 2.8 \)

Answers:
- \( P = 1.4 \)
- \( Q = 2.6 \)
- \( R = 2.8 \)

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#### Number Line 4:
- Scale: The distance between 4 and 5 is divided into 5 equal segments. Each segment represents \( 0.2 \).
- Points:
- \( P \): Located 2 segments after 4.
\( P = 4 + 2 \times 0.2 = 4.4 \)
- \( Q \): Located 1 segment after 4.5.
\( Q = 4.5 + 1 \times 0.2 = 4.7 \)
- \( R \): Located 3 segments after 5.
\( R = 5 + 3 \times 0.2 = 5.6 \)

Answers:
- \( P = 4.4 \)
- \( Q = 4.7 \)
- \( R = 5.6 \)

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Final Answers:

1. Number Line 2:
- \( P = 0.4 \)
- \( Q = 1.7 \)
- \( R = 1.9 \)

2. Number Line 3:
- \( P = 1.4 \)
- \( Q = 2.6 \)
- \( R = 2.8 \)

3. Number Line 4:
- \( P = 4.4 \)
- \( Q = 4.7 \)
- \( R = 5.6 \)

\[
\boxed{
\begin{array}{l}
\text{Number Line 2: } P = 0.4, Q = 1.7, R = 1.9 \\
\text{Number Line 3: } P = 1.4, Q = 2.6, R = 2.8 \\
\text{Number Line 4: } P = 4.4, Q = 4.7, R = 5.6
\end{array}
}
\]